Wood floors are easier on your body and on your dishes. They can be harder to keep up, but, if you use solid instead of engineered wood it will hold up longer. You might also consider using a tile surface at the doorway but not elsewhere?

I've had both, and prefer tile for the maintenance-free attributes. If you use tile, but sure to select a grout that will not show dirt, and seal it before use. My 10 year old tile looks brand new.

Probably no surprise which direction I'd recommend...
But in all honesty, the options in wood flooring nowadays make it a winner all around.

It never goes out of style, is easy to maintain, and is much more forgiving on your back & feet as well as anything dropped on it.

Sure... wood flooring may ding or dent... but tile chips & cracks.
Simple solution is to use a wood flooring that's conducive to high traffic, such as a lightly distressed surface with a GOOD quality polyurethane finish.

We, for example, produce tons of custom options in a wide variety of species, styles, colors, & finishes...
Our Aluminum Oxide polyurethane (which is a proprietary mix) can be chosen in any sheen level and is easy to re-coat at a later date if desired. Very wear & tear friendly as well as water resistant.

As I say REPEATEDLY here on Houzz... the key to making a sound decision in ANY format you choose, is to not let LOW pricing be the determining factor for your final decision. Problem is that it may ALL look the same to the untrained eye... but there is always the "you get what you're willing to pay for" aspect to consider.

Either is a beautiful choice but your lifestyle & taste matters most --- Go for the option you'll be happiest with -- If you love wood and will enjoy it earning history & patina then it's a great fit. If you want the least amount of change over time with the least amount of maintenance, tile may be right for you (just be sure you select something that will not be slippery when wet if your kids are running in from the pool!). The problems that arise with water & wood are usually due to water getting UNDER the wood -- so a floor finished in place with a quality poly & no surface cracks is the best defense.